In T136104#4099980, @WMDE-Fisch wrote:

A similar request in the problem field was reported in https://www.mediawiki.org/wiki/Topic:Uafmytgypbuj7qjg […]

At that URL, see also the quick sketch I made of what a solution (just slightly different from the one stated in the task description) might look like.

It would seem that the suggester now searches labels in all languages, but when searching by item ID (Q…), if there is no label for the UI language, there is still no fallback to any of the user’s other languages. While this might be difficult to implement (requiring analysis of Babel boxes or the like), an easier intermediate solution might be to fall back to official name (P1448) of the suggested item.

re-tested; some behavior has changed for the better, but some issues remain (see updated task description)